Answer:
a. Bisector is at point M
b. [tex]AB = 98[/tex]
Step-by-step explanation:
Question is not well formatted:
Given
[tex]AM = 4x+1[/tex]
[tex]MB = 7x-35[/tex]
Solving (a): The segment bisector
From the given parameters above
We have AM and MB
The common point in AM and MB is M;
This indicates that the bisector is at point M
Solving (b): The value of AB
First we need to determine the value of x
Because M is the point of bisector;
[tex]AM = MB[/tex]
[tex]4x + 1 = 7x - 35[/tex]
Collect Like Terms
[tex]4x - 7x = -1 -35[/tex]
[tex]-3x = -36[/tex]
Solve for x
[tex]x = -36/-3[/tex]
[tex]x =12[/tex]
Next is to determine the value of AB using
[tex]AB = AM + MB[/tex]
[tex]AB = 4x + 1 + 7x - 35[/tex]
Collect Like Terms
[tex]AB = 4x + 7x + 1 - 35[/tex]
[tex]AB = 11x - 34[/tex]
Substitute 12 for x
[tex]AB = 11 * 12 - 34[/tex]
[tex]AB = 132- 34[/tex]
[tex]AB = 98[/tex]
